Question!

This may be a stupid question to some, but does winning with lower * cards against higher * cards still give you more points? I'm thinking it does, but I'm not too sure because it doesn't say anything about it in the DT section of the Game Rules. Thank you!

It doesn't have anything to do with cards on the board. If I understood the rules correctly, it's bonus points awarded for having fewer stars in your entire deck, not just your hand. I may be wrong though.